Target Audience: Any neuroimager using or considering graph theory as a tool for analysing structural or functional brain connectivity. Introduction: Graph theory (GT) is a powerful mathematical framework for quantifying topological properties of networks derived from functional and structural neuroimaging . However, all connectivity inference methods are subject to false positives (FPs), which...

We study cluster algebras with principal coefficient systems that are associated to unpunctured surfaces. We give a direct formula for the Laurent polynomial expansion of cluster variables in these cluster algebras in terms of perfect matchings of a certain graph GT,γ that is constructed from the surface by recursive glueing of elementary pieces that we call tiles. We also give a second formula...

We study cluster algebras with principal coefficient systems that are associated to unpunctured surfaces. We give a direct formula for the Laurent polynomial expansion of cluster variables in these cluster algebras in terms of perfect matchings of a certain graph GT,γ that is constructed from the surface by recursive glueing of elementary pieces that we call tiles. We also give a second formula...

Let G be a chordal graph, X(G) the complement of the associated complex arrangement and Γ(G) the fundamental group of X(G). We show that Γ(G) is a limit of colored braid groups over the poset of simplices of G. When G = GT is the comparability graph associated with a rooted tree T , a case recently investigated by the first author, the result takes the following very simple form: Γ(GT ) is a li...

We study cluster algebras with principal coefficient systems that are associated to unpunctured surfaces. We give a direct formula for the Laurent polynomial expansion of cluster variables in these cluster algebras in terms of perfect matchings of a certain graph GT,γ that is constructed from the surface by recursive glueing of elementary pieces that we call tiles. We also give a second formula...